(NewsNation) — Claims of censorship on Twitter, particularly of right-leaning viewpoints, have gained attention in recent years, sparking lawsuits and even Congressional hearings. Accusations of bias and censorship are largely what prompted Tesla CEO Elon Musk to make a highly publicized offer to buy Twitter for $43 billion.

But is Twitter actually censoring people’s posts based on political ideology?

One new study by professors at MIT and Yale called “Is Twitter Biased Against Conservatives? The Challenge of Inferring Political Bias in a Hyper-Partisan Media Ecosystem” recently took a look.

The authors of the study followed 9,000 politically engaged Twitter users, half Democratic and half Republican, in October 2020. The authors continued keeping track of their Twitter habits for six months after the 2020 election.

The study did find a disparity between how many users from each party were suspended — 7.7% of the Democrats compared to 35.6% of Republicans.

Republicans on Twitter, however, “shared substantially more news from misinformation,” the study found.

David Rand, a management professor at MIT who co-wrote the study, said the report didn’t disprove bias allegations but showed how correlated misinformation sharing and partisanship are.

“Since 2016, [social media] platforms have been under a huge amount of public pressure to act on misinformation,” Rand said. “If they do that, then necessarily, they’re going to wind up sanctioning conservatives more, and it’s going to look like they’re biased against conservatives.”

This can make it seem like there’s “no way” these sites can win, he said.

“If they don’t act on this information, then people are upset about that,” Rand said. “But if they do act on misinformation, then people are upset about the conservatives getting” removed.

Republican users in the study’s dataset shared news from domains that were on average rated as much more untrustworthy by fact-checkers and a survey of politically balanced lay-people than Democratic users, the authors said.

Even with accusations of bias, 80% of the people researchers polled from both parties said social media companies should reduce the spread of misinformation. However, the study noted that people have different definitions of misinformation.

“It’s actually really hard to tell what’s bias and what’s not bias in this current media ecosystem where partisanship and misinformation-sharing are bound up together,” Rand said.

Social media platforms such as Twitter suspend accounts for violating content standards on violence, hate speech and harmful misinformation.

But some question the value in social media sites moderating speech in the first place, and see it as overreach. Conservative author Denise McAllister said in a 2020 interview with USA Today that people needed to be trusted as individuals.

“This is a platform, right? You don’t need to act like mama Twitter or mama Facebook. Just let people say what they are going to say, whether it’s true, false, whatever,” she said.

Musk has also been a vocal critic of Twitter over what he says are problems with free speech.

He’s said that he doesn’t care about making money off Twitter, and wants to buy it because “having a public platform that is maximally trusted and broadly inclusive is extremely important to the future of civilization.”

During a Thursday TED 2022 conference, Musk said he would be “very cautious” on permanent bans, instead opting for “timeouts,” The Hill reported.

“Twitter has become sort of the de facto town square so it’s really important that people have both the reality and the perception that they are able to speak freely within the bounds of the law,” he said, according to The Hill.

There are some hurdles for Musk to leap through if he wants to realize his vision.

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Twitter last week adopted a shareholder rights plan, known as a “poison pill,” that would allow existing Twitter shareholders — besides Musk — to buy additional shares at a discount, diluting the billionaire’s stake. This would make it harder for Musk to get a majority of shareholder votes in favor of his acquisition of the social media platform.